Lagrange Matrices: 3-Body Problem and General

Here is the v2. The Applied Topology and Combinatorics Discussion Group has involved the Lagrange-Democratic Radius of Gyration Lemma for the general N-body Problem. So I now include the equal-masses version of the result here as a ready consequence of the Relative Lagrange Inertia Quadric Lemma. In the v2, these are Lemmas 2 and 1 respectively. I have also added a further part to Exercise 9 involving manipulating the arbitrary-masses version of Lemma 2. Several other Articles make use of Lemma 2.

And here is the original v1.